Function Inverses — Quiz

Question 3 • Mathematics III

If f of x and g of x are inverse functions of each other, which of the following shows the graph of f of g of x ?

Answer

Image with description On a coordinate plane with x and y axes marked from negative 5 to 5, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).

Image with description On a coordinate plane with x and y axes marked from negative 5 to 5, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).

Image with description On a coordinate plane with x and y axes marked from negative 5 to 5, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).

Image with description On a coordinate plane with x and y axes marked from negative 5 to 5, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).

Explanation

Because f and g are inverse functions, applying g and then f returns the original input: f(g(x)) = x. Its graph is the line y = x, which has positive slope 1 and passes through points such as (−3, −3), (0, 0), and (3, 3). That is choice D.

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